Hey there!
The first thing we should do is review the formulas for area and perimeter.
Perimeter can be expressed in two ways: a) l+w+l+w OR b) 2l+2w.
The formula for area is: l*w
We know that the length is 5 feet longer than the width, so when we're defining our variables we can say that width is equal to 'w', and length is equal to 4w+5.
Since we know that the perimeter is equal to 80, we can say that [tex]80= 2(4w+5) + 2(w)[/tex].
Now all we have to do is combine like terms and solve for 80:
[tex]80 = 2(4w+5) +2w [/tex]
[tex]80 = 8w + 10 +2w[/tex]
[tex]80 = 10w +10[/tex]
[tex]80-10 = 10w +10 -10[/tex]
[tex]70 = 10w[/tex]
[tex] \frac{70}{10} = \frac{10w}{10} [/tex]
[tex]7 = w[/tex]
We now know that the width is equal to 7 feet. To find the length, we can substitute the width into 4w+5:
[tex]l = 4w + 5 = 4(7)+5[/tex]
[tex]l = 28 + 5[/tex]
[tex]l = 33[/tex]
Now we know that the length is equal to 33 feet.
So there's your dimensions: 7ft by 33 ft.
Next, to find the area, we take l*w
[tex]33*7 = 231ft^{2} [/tex]
Hope this is helpful! If any of this doesn't make sense or there's more I can help with, please let me know!
